Well, yes, I think this is very clearly what you areaskedto do.

I know that in order to show that Newton's method converges "quadratically" (that is, that the number of valid digits doubles with each iteration), if it converges at all, one does have to do some more fancy guesswork like this. But I think it is obvious that the text of your exercise doesor if I should apply some of this: <more complicated stuff>notrequire you to handle such technicalities.